Run download_data.Rmd and percentage_of_regional_richness.Rmd First!

library(randomForest)
library(reshape2)
library(rpart)
library(ggplot2)
library(tidyverse)

library(multcomp)
library(car)
library(VSURF)

library(boot)
city_data
length(city_data$city_gdp_per_population[!is.na(city_data$city_gdp_per_population)])
[1] 30
length(city_data$percentage_urban_area_as_open_public_spaces[!is.na(city_data$percentage_urban_area_as_open_public_spaces)])
[1] 61
length(city_data$happiness_future_life[!is.na(city_data$happiness_future_life)])
[1] 65
length(city_data$mean_population_exposure_to_pm2_5_2019[!is.na(city_data$mean_population_exposure_to_pm2_5_2019)])
[1] 131
fetch_city_data_for <- function(pool_name, include_city_name = F) {
  results_filename <- paste(paste('percentage_of_regional_richness__output_', pool_name, 'city', 'richness', 'intercept', sep = "_"), "csv", sep = ".")
  results <- read_csv(results_filename)
  
  joined <- left_join(city_data, results)
  
  required_columns <- c("population_growth", "rainfall_monthly_min", "rainfall_annual_average", "rainfall_monthly_max", "temperature_annual_average", "temperature_monthly_min", "temperature_monthly_max", "happiness_negative_effect", "happiness_positive_effect", "happiness_future_life", "number_of_biomes", "realm", "biome_name", "region_20km_includes_estuary", "region_50km_includes_estuary", "region_100km_includes_estuary", "city_includes_estuary", "region_20km_average_pop_density", "region_50km_average_pop_density", "region_100km_average_pop_density", "city_max_pop_density", "city_average_pop_density", "mean_population_exposure_to_pm2_5_2019", "region_20km_cultivated", "region_20km_urban", "region_50km_cultivated", "region_50km_urban", "region_100km_cultivated", "region_100km_urban", "region_20km_elevation_delta", "region_20km_mean_elevation", "region_50km_elevation_delta", "region_50km_mean_elevation", "region_100km_elevation_delta", "region_100km_mean_elevation", "city_elevation_delta", "city_mean_elevation", "urban", "shrubs", "permanent_water", "open_forest", "herbaceous_wetland", "herbaceous_vegetation", "cultivated", "closed_forest", "share_of_population_within_400m_of_open_space", "percentage_urban_area_as_streets", "percentage_urban_area_as_open_public_spaces_and_streets", "percentage_urban_area_as_open_public_spaces", "city_gdp_per_population", "city_ndvi", "city_ssm", "city_susm", "region_20km_ndvi", "region_20km_ssm", "region_20km_susm", "region_50km_ndvi", "region_50km_ssm", "region_50km_susm", "region_100km_ndvi", "region_100km_ssm", "region_100km_susm", "city_percentage_protected", "region_20km_percentage_protected", "region_50km_percentage_protected", "region_100km_percentage_protected", "city_centre_latitude")
  
  if (include_city_name) {
    required_columns <- append(c("name"), required_columns)
  }
  
  required_columns <- append(c("response"), required_columns)
  
  joined[,required_columns]
}
Merlin Response
merlin_city_data <- fetch_city_data_for('merlin')

── Column specification ─────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────
cols(
  name = col_character(),
  response = col_double()
)

Joining, by = "name"
merlin_city_data
merlin_city_data_fixed <- rfImpute(response ~ ., merlin_city_data)
     |      Out-of-bag   |
Tree |      MSE  %Var(y) |
 300 |    21.24   117.83 |
     |      Out-of-bag   |
Tree |      MSE  %Var(y) |
 300 |    20.97   116.32 |
     |      Out-of-bag   |
Tree |      MSE  %Var(y) |
 300 |    21.38   118.61 |
     |      Out-of-bag   |
Tree |      MSE  %Var(y) |
 300 |    21.84   121.18 |
     |      Out-of-bag   |
Tree |      MSE  %Var(y) |
 300 |    21.22   117.73 |
merlin_city_data_fixed
ggplot(merlin_city_data_fixed, aes(response)) + geom_histogram(binwidth = 2)

names(merlin_city_data_fixed)
 [1] "response"                                                "population_growth"                                      
 [3] "rainfall_monthly_min"                                    "rainfall_annual_average"                                
 [5] "rainfall_monthly_max"                                    "temperature_annual_average"                             
 [7] "temperature_monthly_min"                                 "temperature_monthly_max"                                
 [9] "happiness_negative_effect"                               "happiness_positive_effect"                              
[11] "happiness_future_life"                                   "number_of_biomes"                                       
[13] "realm"                                                   "biome_name"                                             
[15] "region_20km_includes_estuary"                            "region_50km_includes_estuary"                           
[17] "region_100km_includes_estuary"                           "city_includes_estuary"                                  
[19] "region_20km_average_pop_density"                         "region_50km_average_pop_density"                        
[21] "region_100km_average_pop_density"                        "city_max_pop_density"                                   
[23] "city_average_pop_density"                                "mean_population_exposure_to_pm2_5_2019"                 
[25] "region_20km_cultivated"                                  "region_20km_urban"                                      
[27] "region_50km_cultivated"                                  "region_50km_urban"                                      
[29] "region_100km_cultivated"                                 "region_100km_urban"                                     
[31] "region_20km_elevation_delta"                             "region_20km_mean_elevation"                             
[33] "region_50km_elevation_delta"                             "region_50km_mean_elevation"                             
[35] "region_100km_elevation_delta"                            "region_100km_mean_elevation"                            
[37] "city_elevation_delta"                                    "city_mean_elevation"                                    
[39] "urban"                                                   "shrubs"                                                 
[41] "permanent_water"                                         "open_forest"                                            
[43] "herbaceous_wetland"                                      "herbaceous_vegetation"                                  
[45] "cultivated"                                              "closed_forest"                                          
[47] "share_of_population_within_400m_of_open_space"           "percentage_urban_area_as_streets"                       
[49] "percentage_urban_area_as_open_public_spaces_and_streets" "percentage_urban_area_as_open_public_spaces"            
[51] "city_gdp_per_population"                                 "city_ndvi"                                              
[53] "city_ssm"                                                "city_susm"                                              
[55] "region_20km_ndvi"                                        "region_20km_ssm"                                        
[57] "region_20km_susm"                                        "region_50km_ndvi"                                       
[59] "region_50km_ssm"                                         "region_50km_susm"                                       
[61] "region_100km_ndvi"                                       "region_100km_ssm"                                       
[63] "region_100km_susm"                                       "city_percentage_protected"                              
[65] "region_20km_percentage_protected"                        "region_50km_percentage_protected"                       
[67] "region_100km_percentage_protected"                       "city_centre_latitude"                                   
merlin_response <- merlin_city_data_fixed$response
merlin_predictors <- merlin_city_data_fixed[,-1]
merlin_predictors
merlin_interp <- VSURF(x = merlin_predictors, y  = merlin_response)
Thresholding step
Estimated computational time (on one core): 118.3 sec.

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Interpretation step (on 34 variables)
Estimated computational time (on one core): between 42.5 sec. and  234.6 sec.

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Prediction step (on 4 variables)
Maximum estimated computational time (on one core): 5.3 sec.

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names(merlin_predictors[,merlin_interp$varselect.interp])
[1] "region_50km_elevation_delta" "region_50km_ssm"             "biome_name"                  "region_100km_ssm"           
Birdlife Response
birdlife_city_data <- fetch_city_data_for('birdlife')

── Column specification ─────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────
cols(
  name = col_character(),
  response = col_double()
)

Joining, by = "name"
birdlife_city_data
ggplot(birdlife_city_data, aes(response)) + geom_histogram(binwidth = 1)

birdlife_city_data_fixed <- rfImpute(response ~ ., birdlife_city_data)
     |      Out-of-bag   |
Tree |      MSE  %Var(y) |
 300 |    5.895    93.31 |
     |      Out-of-bag   |
Tree |      MSE  %Var(y) |
 300 |    5.618    88.93 |
     |      Out-of-bag   |
Tree |      MSE  %Var(y) |
 300 |    5.764    91.24 |
     |      Out-of-bag   |
Tree |      MSE  %Var(y) |
 300 |    5.757    91.14 |
     |      Out-of-bag   |
Tree |      MSE  %Var(y) |
 300 |    5.725    90.63 |
birdlife_city_data_fixed
names(merlin_city_data_fixed)
 [1] "response"                                                "population_growth"                                      
 [3] "rainfall_monthly_min"                                    "rainfall_annual_average"                                
 [5] "rainfall_monthly_max"                                    "temperature_annual_average"                             
 [7] "temperature_monthly_min"                                 "temperature_monthly_max"                                
 [9] "happiness_negative_effect"                               "happiness_positive_effect"                              
[11] "happiness_future_life"                                   "number_of_biomes"                                       
[13] "realm"                                                   "biome_name"                                             
[15] "region_20km_includes_estuary"                            "region_50km_includes_estuary"                           
[17] "region_100km_includes_estuary"                           "city_includes_estuary"                                  
[19] "region_20km_average_pop_density"                         "region_50km_average_pop_density"                        
[21] "region_100km_average_pop_density"                        "city_max_pop_density"                                   
[23] "city_average_pop_density"                                "mean_population_exposure_to_pm2_5_2019"                 
[25] "region_20km_cultivated"                                  "region_20km_urban"                                      
[27] "region_50km_cultivated"                                  "region_50km_urban"                                      
[29] "region_100km_cultivated"                                 "region_100km_urban"                                     
[31] "region_20km_elevation_delta"                             "region_20km_mean_elevation"                             
[33] "region_50km_elevation_delta"                             "region_50km_mean_elevation"                             
[35] "region_100km_elevation_delta"                            "region_100km_mean_elevation"                            
[37] "city_elevation_delta"                                    "city_mean_elevation"                                    
[39] "urban"                                                   "shrubs"                                                 
[41] "permanent_water"                                         "open_forest"                                            
[43] "herbaceous_wetland"                                      "herbaceous_vegetation"                                  
[45] "cultivated"                                              "closed_forest"                                          
[47] "share_of_population_within_400m_of_open_space"           "percentage_urban_area_as_streets"                       
[49] "percentage_urban_area_as_open_public_spaces_and_streets" "percentage_urban_area_as_open_public_spaces"            
[51] "city_gdp_per_population"                                 "city_ndvi"                                              
[53] "city_ssm"                                                "city_susm"                                              
[55] "region_20km_ndvi"                                        "region_20km_ssm"                                        
[57] "region_20km_susm"                                        "region_50km_ndvi"                                       
[59] "region_50km_ssm"                                         "region_50km_susm"                                       
[61] "region_100km_ndvi"                                       "region_100km_ssm"                                       
[63] "region_100km_susm"                                       "city_percentage_protected"                              
[65] "region_20km_percentage_protected"                        "region_50km_percentage_protected"                       
[67] "region_100km_percentage_protected"                       "city_centre_latitude"                                   
birdlife_response <- birdlife_city_data_fixed$response
birdlife_predictors <- birdlife_city_data_fixed[,-1]
birdlife_predictors
birdlife_interp <- VSURF(x = birdlife_predictors, y  = birdlife_response)
Thresholding step
Estimated computational time (on one core): 103.7 sec.

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Interpretation step (on 53 variables)
Estimated computational time (on one core): between 70.2 sec. and  482.3 sec.

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Prediction step (on 2 variables)
Maximum estimated computational time (on one core): 2.5 sec.

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names(birdlife_predictors[,birdlife_interp$varselect.interp])
[1] "population_growth" "region_50km_ssm"  
So….
Merlin: “region_50km_elevation_delta” “biome_name” “region_50km_ssm” “region_100km_ssm” Birdlife: “population_growth” “region_50km_ssm”

Try Modelling

merlin_city_data_named <- fetch_city_data_for('merlin', T)

── Column specification ─────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────
cols(
  name = col_character(),
  response = col_double()
)

Joining, by = "name"
birdlife_city_data_named <- fetch_city_data_for('birdlife', T)

── Column specification ─────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────
cols(
  name = col_character(),
  response = col_double()
)

Joining, by = "name"
Use cross validation and dropping terms to find best model

full model: response ~ region_100km_ssm + region_50km_ssm + region_50km_elevation_delta + biome_name + population_growth

Merlin data set

merlin_city_data_fixed_no_boreal <- merlin_city_data_fixed[merlin_city_data_fixed$biome_name != 'Boreal Forests/Taiga',]
cv.glm(merlin_city_data_fixed_no_boreal, glm(formula = response ~ region_100km_ssm + region_50km_ssm + region_50km_elevation_delta + biome_name + population_growth, data = merlin_city_data_fixed_no_boreal))$delta[1]
[1] 19.72841

– CVE 19.72841 – Can we drop one?

cv.glm(merlin_city_data_fixed_no_boreal, glm(formula = response ~ region_50km_ssm + region_50km_elevation_delta + biome_name + population_growth, data = merlin_city_data_fixed_no_boreal))$delta[1]
[1] 19.39392
cv.glm(merlin_city_data_fixed_no_boreal, glm(formula = response ~ region_100km_ssm + region_50km_elevation_delta + biome_name + population_growth, data = merlin_city_data_fixed_no_boreal))$delta[1]
[1] 19.3626
cv.glm(merlin_city_data_fixed_no_boreal, glm(formula = response ~ region_100km_ssm + region_50km_ssm + biome_name + population_growth, data = merlin_city_data_fixed_no_boreal))$delta[1]
[1] 19.79173
cv.glm(merlin_city_data_fixed_no_boreal, glm(formula = response ~ region_100km_ssm + region_50km_ssm + region_50km_elevation_delta + population_growth, data = merlin_city_data_fixed_no_boreal))$delta[1]
[1] 18.53183
cv.glm(merlin_city_data_fixed_no_boreal, glm(formula = response ~ region_100km_ssm + region_50km_ssm + region_50km_elevation_delta + biome_name, data = merlin_city_data_fixed_no_boreal))$delta[1]
[1] 19.38052

– drop biome_name to give smaller CVE of 18.53183 – can we drop another?

cv.glm(merlin_city_data_fixed_no_boreal, glm(formula = response ~ region_50km_ssm + region_50km_elevation_delta + population_growth, data = merlin_city_data_fixed_no_boreal))$delta[1]
[1] 18.26184
cv.glm(merlin_city_data_fixed_no_boreal, glm(formula = response ~ region_100km_ssm + region_50km_elevation_delta + population_growth, data = merlin_city_data_fixed_no_boreal))$delta[1]
[1] 18.24017
cv.glm(merlin_city_data_fixed_no_boreal, glm(formula = response ~ region_100km_ssm + region_50km_ssm + population_growth, data = merlin_city_data_fixed_no_boreal))$delta[1]
[1] 18.79038
cv.glm(merlin_city_data_fixed_no_boreal, glm(formula = response ~ region_100km_ssm + region_50km_ssm + region_50km_elevation_delta, data = merlin_city_data_fixed_no_boreal))$delta[1]
[1] 18.20095

– drop population_growth to give CVE of 18.20095 – can we drop another?

cv.glm(merlin_city_data_fixed_no_boreal, glm(formula = response ~ region_50km_ssm + region_50km_elevation_delta, data = merlin_city_data_fixed_no_boreal))$delta[1]
[1] 17.9362
cv.glm(merlin_city_data_fixed_no_boreal, glm(formula = response ~ region_100km_ssm + region_50km_elevation_delta, data = merlin_city_data_fixed_no_boreal))$delta[1]
[1] 17.91216
cv.glm(merlin_city_data_fixed_no_boreal, glm(formula = response ~ region_100km_ssm + region_50km_ssm, data = merlin_city_data_fixed_no_boreal))$delta[1]
[1] 18.48549

– drop region_50km_ssm to give CVE of 17.91216 – can we drop another?

cv.glm(merlin_city_data_fixed_no_boreal, glm(formula = response ~ region_100km_ssm, data = merlin_city_data_fixed_no_boreal))$delta[1]
[1] 18.19515
cv.glm(merlin_city_data_fixed_no_boreal, glm(formula = response ~ region_50km_elevation_delta, data = merlin_city_data_fixed_no_boreal))$delta[1]
[1] 18.04985
– best model with region_100km_ssm + region_50km_elevation_delta (CV error 17.91216)
summary(glm(data = merlin_city_data_fixed, formula = response ~ region_100km_ssm + region_50km_elevation_delta))

Call:
glm(formula = response ~ region_100km_ssm + region_50km_elevation_delta, 
    data = merlin_city_data_fixed)

Deviance Residuals: 
    Min       1Q   Median       3Q      Max  
-7.6599  -2.9987  -0.5524   1.7449  16.9143  

Coefficients:
                              Estimate Std. Error t value Pr(>|t|)  
(Intercept)                  2.6809304  1.1210300   2.391   0.0182 *
region_100km_ssm            -0.1331207  0.0695604  -1.914   0.0578 .
region_50km_elevation_delta -0.0006899  0.0003461  -1.994   0.0482 *
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

(Dispersion parameter for gaussian family taken to be 17.36262)

    Null deviance: 2469.6  on 136  degrees of freedom
Residual deviance: 2326.6  on 134  degrees of freedom
AIC: 784.8

Number of Fisher Scoring iterations: 2
reg_merlin = glm(data = merlin_city_data_fixed, formula = response ~ region_100km_ssm + region_50km_elevation_delta)
with(summary(reg_merlin), 1 - deviance/null.deviance)
[1] 0.05791102

Birdlife data set

birdlife_city_data_fixed_no_boreal <- birdlife_city_data_fixed[birdlife_city_data_fixed$biome_name != 'Boreal Forests/Taiga',]
cv.glm(birdlife_city_data_fixed_no_boreal, glm(formula = response ~ region_100km_ssm + region_50km_ssm + region_50km_elevation_delta + biome_name + population_growth, data = birdlife_city_data_fixed_no_boreal))$delta[1]
[1] 6.899862

– can we drop a variable?

cv.glm(birdlife_city_data_fixed_no_boreal, glm(formula = response ~ region_50km_ssm + region_50km_elevation_delta + biome_name + population_growth, data = birdlife_city_data_fixed_no_boreal))$delta[1]
[1] 6.768164
cv.glm(birdlife_city_data_fixed_no_boreal, glm(formula = response ~ region_100km_ssm + region_50km_elevation_delta + biome_name + population_growth, data = birdlife_city_data_fixed_no_boreal))$delta[1]
[1] 6.752211
cv.glm(birdlife_city_data_fixed_no_boreal, glm(formula = response ~ region_100km_ssm + region_50km_ssm + biome_name + population_growth, data = birdlife_city_data_fixed_no_boreal))$delta[1]
[1] 6.989636
cv.glm(birdlife_city_data_fixed_no_boreal, glm(formula = response ~ region_100km_ssm + region_50km_ssm + region_50km_elevation_delta + population_growth, data = birdlife_city_data_fixed_no_boreal))$delta[1]
[1] 6.503421
cv.glm(birdlife_city_data_fixed_no_boreal, glm(formula = response ~ region_100km_ssm + region_50km_ssm + region_50km_elevation_delta + biome_name, data = birdlife_city_data_fixed_no_boreal))$delta[1]
[1] 6.780578

– drop biome_name to give CVE of 6.503421 – can we drop another?

cv.glm(birdlife_city_data_fixed_no_boreal, glm(formula = response ~ region_50km_ssm + region_50km_elevation_delta + population_growth, data = birdlife_city_data_fixed_no_boreal))$delta[1]
[1] 6.417311
cv.glm(birdlife_city_data_fixed_no_boreal, glm(formula = response ~ region_100km_ssm + region_50km_elevation_delta + population_growth, data = birdlife_city_data_fixed_no_boreal))$delta[1]
[1] 6.426562
cv.glm(birdlife_city_data_fixed_no_boreal, glm(formula = response ~ region_100km_ssm + region_50km_ssm + population_growth, data = birdlife_city_data_fixed_no_boreal))$delta[1]
[1] 6.430742
cv.glm(birdlife_city_data_fixed_no_boreal, glm(formula = response ~ region_100km_ssm + region_50km_ssm + region_50km_elevation_delta, data = birdlife_city_data_fixed_no_boreal))$delta[1]
[1] 6.439714

– drop region_100km_ssm to give CVE of 6.417311 – can we drop another?

cv.glm(birdlife_city_data_fixed_no_boreal, glm(formula = response ~ region_50km_elevation_delta + population_growth, data = birdlife_city_data_fixed_no_boreal))$delta[1]
[1] 6.535285
cv.glm(birdlife_city_data_fixed_no_boreal, glm(formula = response ~ region_50km_ssm + population_growth, data = birdlife_city_data_fixed_no_boreal))$delta[1]
[1] 6.342025
cv.glm(birdlife_city_data_fixed_no_boreal, glm(formula = response ~ region_50km_ssm + region_50km_elevation_delta, data = birdlife_city_data_fixed_no_boreal))$delta[1]
[1] 6.352664

– drop region_50km_elevation_delta to give CVE of 6.342025 – can we drop another?

cv.glm(birdlife_city_data_fixed_no_boreal, glm(formula = response ~ population_growth, data = birdlife_city_data_fixed_no_boreal))$delta[1]
[1] 6.464699
cv.glm(birdlife_city_data_fixed_no_boreal, glm(formula = response ~ region_50km_ssm, data = birdlife_city_data_fixed_no_boreal))$delta[1]
[1] 6.291299

– drop city_gdp_per_population to give CVE of 6.291299 – is this better than no variable?

cv.glm(birdlife_city_data_fixed_no_boreal, glm(formula = response ~ 1, data = birdlife_city_data_fixed_no_boreal))$delta[1]
[1] 6.395701

– yes, just!

– so best model with birdlife is region_50km_ssm
summary(glm(data = birdlife_city_data_fixed, formula = response ~ region_50km_ssm))

Call:
glm(formula = response ~ region_50km_ssm, data = birdlife_city_data_fixed)

Deviance Residuals: 
    Min       1Q   Median       3Q      Max  
-4.5353  -1.5461  -0.4124   1.3071  10.7572  

Coefficients:
                Estimate Std. Error t value Pr(>|t|)  
(Intercept)      1.26916    0.65041   1.951   0.0531 .
region_50km_ssm -0.08499    0.04115  -2.065   0.0408 *
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

(Dispersion parameter for gaussian family taken to be 6.214378)

    Null deviance: 865.45  on 136  degrees of freedom
Residual deviance: 838.94  on 135  degrees of freedom
AIC: 643.06

Number of Fisher Scoring iterations: 2
reg_birdlife = glm(data = birdlife_city_data_fixed, formula = response ~ region_50km_ssm)
with(summary(reg_birdlife), 1 - deviance/null.deviance)
[1] 0.03062471
ggplot(birdlife_city_data_named, aes(x = region_50km_ssm, y = response)) + geom_point() + geom_smooth(method = "glm")
`geom_smooth()` using formula 'y ~ x'

Check birdlife model fit
birdlife.fit <- glm(data = birdlife_city_data_fixed, formula = response ~ region_50km_ssm)
summary(birdlife.fit)

Call:
glm(formula = response ~ region_50km_ssm, data = birdlife_city_data_fixed)

Deviance Residuals: 
    Min       1Q   Median       3Q      Max  
-4.5353  -1.5461  -0.4124   1.3071  10.7572  

Coefficients:
                Estimate Std. Error t value Pr(>|t|)  
(Intercept)      1.26916    0.65041   1.951   0.0531 .
region_50km_ssm -0.08499    0.04115  -2.065   0.0408 *
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

(Dispersion parameter for gaussian family taken to be 6.214378)

    Null deviance: 865.45  on 136  degrees of freedom
Residual deviance: 838.94  on 135  degrees of freedom
AIC: 643.06

Number of Fisher Scoring iterations: 2
with(summary(birdlife.fit), 1 - deviance/null.deviance)
[1] 0.03062471
plot(birdlife.fit)

birdlife_city_data_fixed_no_boreal[c(16, 53, 72), c("region_50km_ssm")]
[1] 18.451180  9.961682 11.644862
city_data[c(16, 53, 72), c("name", "region_50km_ssm")]
dat <- predict(glm(formula = response ~ region_50km_ssm, data = birdlife_city_data_named), se.fit=T)

outside_se <- birdlife_city_data_named[birdlife_city_data_named$response < dat$fit - 15* dat$se.fit | birdlife_city_data_named$response > dat$fit + 15 * dat$se.fit,]

ggplot(birdlife_city_data_named, aes(x = region_50km_ssm, y = response)) + 
  geom_point(size=1) + 
  geom_smooth(method = "glm") +
  geom_text(aes(label = name), data = outside_se, size = 3, position = "dodge", vjust = "inward", hjust = "inward", color = "red", angle=-15) +
  geom_point(data = outside_se, color = "red") +
  theme_bw() +
  ylab("City Random Effect Intercept") + xlab("Regional (50km) SSM") + labs(title = "Birdlife")
`geom_smooth()` using formula 'y ~ x'
Warning: Width not defined. Set with `position_dodge(width = ?)`
ggsave("city_effect_richness__output__birdlife.jpg")
Saving 7.29 x 4.51 in image
`geom_smooth()` using formula 'y ~ x'
Warning: Width not defined. Set with `position_dodge(width = ?)`

How much variation have we explained?

birdlife_city_data_named$residuals <- resid(birdlife.fit)
ggplot(birdlife_city_data_named, aes(y = response, x = residuals)) + 
  geom_point() +
  geom_smooth(method = "lm", se = F) +
  labs(title = "Birdlife", subtitle = paste("Correlation", cor(birdlife_city_data_named$residuals, birdlife_city_data_named$response))) +
  theme_bw()
`geom_smooth()` using formula 'y ~ x'

Check Merlin model fit
merlin.fit <- glm(data = merlin_city_data_named, formula = response ~ region_100km_ssm + region_50km_elevation_delta)
summary(merlin.fit)

Call:
glm(formula = response ~ region_100km_ssm + region_50km_elevation_delta, 
    data = merlin_city_data_named)

Deviance Residuals: 
    Min       1Q   Median       3Q      Max  
-7.6599  -2.9987  -0.5524   1.7449  16.9143  

Coefficients:
                              Estimate Std. Error t value Pr(>|t|)  
(Intercept)                  2.6809304  1.1210300   2.391   0.0182 *
region_100km_ssm            -0.1331207  0.0695604  -1.914   0.0578 .
region_50km_elevation_delta -0.0006899  0.0003461  -1.994   0.0482 *
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

(Dispersion parameter for gaussian family taken to be 17.36262)

    Null deviance: 2469.6  on 136  degrees of freedom
Residual deviance: 2326.6  on 134  degrees of freedom
AIC: 784.8

Number of Fisher Scoring iterations: 2
with(summary(merlin.fit), 1 - deviance/null.deviance)
[1] 0.05791102
plot(merlin.fit)

merlin_city_data_fixed_no_boreal[c(24, 42, 72), c("region_100km_ssm", "region_50km_elevation_delta")]
city_data[c(24, 42, 72), c("name", "region_100km_ssm", "region_50km_elevation_delta")]
ggplot(merlin_city_data_named, aes(x = region_100km_ssm, y = response)) + 
  geom_point(aes(size = region_50km_elevation_delta)) + 
  geom_smooth(method = "glm") +
  theme_bw() +
  theme(legend.position="bottom") +
  ylab("City Random Effect Intercept") + xlab("Regional (100km) SSM") + labs(title = "eBird") + guides(size=guide_legend(title="Regional (50km) Elevation Delta"))
`geom_smooth()` using formula 'y ~ x'
ggsave("city_effect_richness__output__merlin.jpg")
Saving 7.29 x 4.51 in image
`geom_smooth()` using formula 'y ~ x'

How much variation have we explained?

merlin_city_data_named$residuals <- resid(merlin.fit)
ggplot(merlin_city_data_named, aes(y = response, x = residuals)) + 
  geom_point() +
  geom_smooth(method = "lm", se = F) +
  labs(title = "Merlin", subtitle = paste("Correlation", cor(merlin_city_data_named$residuals, merlin_city_data_named$response))) +
  theme_bw()
`geom_smooth()` using formula 'y ~ x'

Check AIC
AIC(
  glm(data = merlin_city_data_fixed, formula = response ~ region_100km_ssm + region_50km_ssm + region_50km_elevation_delta + biome_name + population_growth),
  glm(data = merlin_city_data_fixed, formula = response ~ region_100km_ssm + region_50km_elevation_delta)
)
AIC(
  glm(data = birdlife_city_data_fixed, formula = response ~ region_100km_ssm + region_50km_ssm + region_50km_elevation_delta + biome_name + population_growth),
  glm(data = birdlife_city_data_fixed, formula = response ~ region_50km_ssm)
)
LDG
birdlife_data_with_lat = fetch_city_data_for('birdlife', include_city_name = T)

── Column specification ─────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────
cols(
  name = col_character(),
  response = col_double()
)

Joining, by = "name"
dat2 <- predict(glm(formula = response ~ city_centre_latitude, data = birdlife_data_with_lat), se.fit=T)

outside_se <- birdlife_data_with_lat[birdlife_data_with_lat$response < dat2$fit - 15* dat2$se.fit | birdlife_data_with_lat$response > dat2$fit + 15 * dat2$se.fit,]

ggplot(birdlife_data_with_lat, aes(x = city_centre_latitude, y = response)) + 
  geom_point(size=1) + 
  geom_smooth(method = "glm", formula = y ~ I(x^2)) +
  geom_text(aes(label = name), data = outside_se, size = 3, position = "dodge", vjust = "inward", hjust = "inward", color = "red", angle=-15) +
  geom_point(data = outside_se, color = "red") +
  theme_bw() +
  ylab("City Random Effect Intercept") + xlab("Latitude (of city centre)") + labs(title = "Birdlife")
Warning: Width not defined. Set with `position_dodge(width = ?)`
ggsave('city_effect_richness__output__ldg_birdlife.jpg')
Saving 7.29 x 4.51 in image
Warning: Width not defined. Set with `position_dodge(width = ?)`

merlin_data_with_lat = fetch_city_data_for('merlin', include_city_name = T)

── Column specification ─────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────
cols(
  name = col_character(),
  response = col_double()
)

Joining, by = "name"
dat2 <- predict(glm(formula = response ~ city_centre_latitude, data = merlin_data_with_lat), se.fit=T)

outside_se <- merlin_data_with_lat[merlin_data_with_lat$response < dat2$fit - 15* dat2$se.fit | merlin_data_with_lat$response > dat2$fit + 15 * dat2$se.fit,]

ggplot(merlin_data_with_lat, aes(x = city_centre_latitude, y = response)) + 
  geom_point(size=1) + 
  geom_smooth(method = "glm", formula = y ~ I(x^2)) +
  geom_text(aes(label = name), data = outside_se, size = 3, position = "dodge", vjust = "inward", hjust = "inward", color = "red", angle=-15) +
  geom_point(data = outside_se, color = "red") +
  theme_bw() +
  ylab("City Random Effect Intercept") + xlab("Latitude (of city centre)") + labs(title = "eBird")
Warning: Width not defined. Set with `position_dodge(width = ?)`
ggsave('city_effect_richness__output__ldg_merlin.jpg')
Saving 7.29 x 4.51 in image
Warning: Width not defined. Set with `position_dodge(width = ?)`

---
title: "R Notebook"
output: html_notebook
---
Run `download_data.Rmd` and `percentage_of_regional_richness.Rmd` First!

```{r setup}
library(randomForest)
library(reshape2)
library(rpart)
library(ggplot2)
library(tidyverse)

library(multcomp)
library(car)
library(VSURF)

library(boot)
```

```{r}
city_data
```

```{r}
length(city_data$city_gdp_per_population[!is.na(city_data$city_gdp_per_population)])
length(city_data$percentage_urban_area_as_open_public_spaces[!is.na(city_data$percentage_urban_area_as_open_public_spaces)])
length(city_data$happiness_future_life[!is.na(city_data$happiness_future_life)])
length(city_data$mean_population_exposure_to_pm2_5_2019[!is.na(city_data$mean_population_exposure_to_pm2_5_2019)])
```

```{r}
fetch_city_data_for <- function(pool_name, include_city_name = F) {
  results_filename <- paste(paste('percentage_of_regional_richness__output_', pool_name, 'city', 'richness', 'intercept', sep = "_"), "csv", sep = ".")
  results <- read_csv(results_filename)
  
  joined <- left_join(city_data, results)
  
  required_columns <- c("population_growth", "rainfall_monthly_min", "rainfall_annual_average", "rainfall_monthly_max", "temperature_annual_average", "temperature_monthly_min", "temperature_monthly_max", "happiness_negative_effect", "happiness_positive_effect", "happiness_future_life", "number_of_biomes", "realm", "biome_name", "region_20km_includes_estuary", "region_50km_includes_estuary", "region_100km_includes_estuary", "city_includes_estuary", "region_20km_average_pop_density", "region_50km_average_pop_density", "region_100km_average_pop_density", "city_max_pop_density", "city_average_pop_density", "mean_population_exposure_to_pm2_5_2019", "region_20km_cultivated", "region_20km_urban", "region_50km_cultivated", "region_50km_urban", "region_100km_cultivated", "region_100km_urban", "region_20km_elevation_delta", "region_20km_mean_elevation", "region_50km_elevation_delta", "region_50km_mean_elevation", "region_100km_elevation_delta", "region_100km_mean_elevation", "city_elevation_delta", "city_mean_elevation", "urban", "shrubs", "permanent_water", "open_forest", "herbaceous_wetland", "herbaceous_vegetation", "cultivated", "closed_forest", "share_of_population_within_400m_of_open_space", "percentage_urban_area_as_streets", "percentage_urban_area_as_open_public_spaces_and_streets", "percentage_urban_area_as_open_public_spaces", "city_gdp_per_population", "city_ndvi", "city_ssm", "city_susm", "region_20km_ndvi", "region_20km_ssm", "region_20km_susm", "region_50km_ndvi", "region_50km_ssm", "region_50km_susm", "region_100km_ndvi", "region_100km_ssm", "region_100km_susm", "city_percentage_protected", "region_20km_percentage_protected", "region_50km_percentage_protected", "region_100km_percentage_protected", "city_centre_latitude")
  
  if (include_city_name) {
    required_columns <- append(c("name"), required_columns)
  }
  
  required_columns <- append(c("response"), required_columns)
  
  joined[,required_columns]
}
```


----------------------
Merlin Response
----------------------

```{r}
merlin_city_data <- fetch_city_data_for('merlin')
merlin_city_data
```

```{r}
merlin_city_data_fixed <- rfImpute(response ~ ., merlin_city_data)
merlin_city_data_fixed
```

```{r}
ggplot(merlin_city_data_fixed, aes(response)) + geom_histogram(binwidth = 2)
```

```{r}
names(merlin_city_data_fixed)
```

```{r}
merlin_response <- merlin_city_data_fixed$response
merlin_predictors <- merlin_city_data_fixed[,-1]
merlin_predictors
```

```{r}
merlin_interp <- VSURF(x = merlin_predictors, y  = merlin_response)
```

```{r}
names(merlin_predictors[,merlin_interp$varselect.interp])
```

----------------------
Birdlife Response
----------------------
```{r}
birdlife_city_data <- fetch_city_data_for('birdlife')
birdlife_city_data
```



```{r}
ggplot(birdlife_city_data, aes(response)) + geom_histogram(binwidth = 1)
```

```{r}
birdlife_city_data_fixed <- rfImpute(response ~ ., birdlife_city_data)
birdlife_city_data_fixed
```

```{r}
names(merlin_city_data_fixed)
```

```{r}
birdlife_response <- birdlife_city_data_fixed$response
birdlife_predictors <- birdlife_city_data_fixed[,-1]
birdlife_predictors
```


```{r}
birdlife_interp <- VSURF(x = birdlife_predictors, y  = birdlife_response)
```

```{r}
names(birdlife_predictors[,birdlife_interp$varselect.interp])
```


------------------------------------------
So....
------------------------------------------
Merlin: "region_50km_elevation_delta" "biome_name" "region_50km_ssm" "region_100km_ssm"
Birdlife: "population_growth" "region_50km_ssm"  

-----------------------------
Try Modelling
-----------------------------


```{r}
merlin_city_data_named <- fetch_city_data_for('merlin', T)
birdlife_city_data_named <- fetch_city_data_for('birdlife', T)
```

------------------------------------------------------------------
Use cross validation and dropping terms to find best model
------------------------------------------------------------------

full model:  response ~ region_100km_ssm + region_50km_ssm + region_50km_elevation_delta + biome_name + population_growth


Merlin data set
----------------
```{r}
merlin_city_data_fixed_no_boreal <- merlin_city_data_fixed[merlin_city_data_fixed$biome_name != 'Boreal Forests/Taiga',]
```

```{r}
cv.glm(merlin_city_data_fixed_no_boreal, glm(formula = response ~ region_100km_ssm + region_50km_ssm + region_50km_elevation_delta + biome_name + population_growth, data = merlin_city_data_fixed_no_boreal))$delta[1]
```

-- CVE 19.72841
-- Can we drop one?

```{r}
cv.glm(merlin_city_data_fixed_no_boreal, glm(formula = response ~ region_50km_ssm + region_50km_elevation_delta + biome_name + population_growth, data = merlin_city_data_fixed_no_boreal))$delta[1]
```

```{r}
cv.glm(merlin_city_data_fixed_no_boreal, glm(formula = response ~ region_100km_ssm + region_50km_elevation_delta + biome_name + population_growth, data = merlin_city_data_fixed_no_boreal))$delta[1]
```

```{r}
cv.glm(merlin_city_data_fixed_no_boreal, glm(formula = response ~ region_100km_ssm + region_50km_ssm + biome_name + population_growth, data = merlin_city_data_fixed_no_boreal))$delta[1]
```

```{r}
cv.glm(merlin_city_data_fixed_no_boreal, glm(formula = response ~ region_100km_ssm + region_50km_ssm + region_50km_elevation_delta + population_growth, data = merlin_city_data_fixed_no_boreal))$delta[1]
```

```{r}
cv.glm(merlin_city_data_fixed_no_boreal, glm(formula = response ~ region_100km_ssm + region_50km_ssm + region_50km_elevation_delta + biome_name, data = merlin_city_data_fixed_no_boreal))$delta[1]
```

-- drop biome_name to give smaller CVE of 18.53183
-- can we drop another?

```{r}
cv.glm(merlin_city_data_fixed_no_boreal, glm(formula = response ~ region_50km_ssm + region_50km_elevation_delta + population_growth, data = merlin_city_data_fixed_no_boreal))$delta[1]
```

```{r}
cv.glm(merlin_city_data_fixed_no_boreal, glm(formula = response ~ region_100km_ssm + region_50km_elevation_delta + population_growth, data = merlin_city_data_fixed_no_boreal))$delta[1]
```

```{r}
cv.glm(merlin_city_data_fixed_no_boreal, glm(formula = response ~ region_100km_ssm + region_50km_ssm + population_growth, data = merlin_city_data_fixed_no_boreal))$delta[1]
```

```{r}
cv.glm(merlin_city_data_fixed_no_boreal, glm(formula = response ~ region_100km_ssm + region_50km_ssm + region_50km_elevation_delta, data = merlin_city_data_fixed_no_boreal))$delta[1]
```

-- drop population_growth to give CVE of 18.20095
-- can we drop another?

```{r}
cv.glm(merlin_city_data_fixed_no_boreal, glm(formula = response ~ region_50km_ssm + region_50km_elevation_delta, data = merlin_city_data_fixed_no_boreal))$delta[1]
```

```{r}
cv.glm(merlin_city_data_fixed_no_boreal, glm(formula = response ~ region_100km_ssm + region_50km_elevation_delta, data = merlin_city_data_fixed_no_boreal))$delta[1]
```

```{r}
cv.glm(merlin_city_data_fixed_no_boreal, glm(formula = response ~ region_100km_ssm + region_50km_ssm, data = merlin_city_data_fixed_no_boreal))$delta[1]
```

-- drop region_50km_ssm to give CVE of 17.91216
-- can we drop another?

```{r}
cv.glm(merlin_city_data_fixed_no_boreal, glm(formula = response ~ region_100km_ssm, data = merlin_city_data_fixed_no_boreal))$delta[1]
```

```{r}
cv.glm(merlin_city_data_fixed_no_boreal, glm(formula = response ~ region_50km_elevation_delta, data = merlin_city_data_fixed_no_boreal))$delta[1]
```


----------------------------------------------------------------------------------------------
-- best model with region_100km_ssm + region_50km_elevation_delta (CV error 17.91216)
----------------------------------------------------------------------------------------------

```{r}
summary(glm(data = merlin_city_data_fixed, formula = response ~ region_100km_ssm + region_50km_elevation_delta))
```

```{r}
reg_merlin = glm(data = merlin_city_data_fixed, formula = response ~ region_100km_ssm + region_50km_elevation_delta)
with(summary(reg_merlin), 1 - deviance/null.deviance)
```

Birdlife data set
----------------
```{r}
birdlife_city_data_fixed_no_boreal <- birdlife_city_data_fixed[birdlife_city_data_fixed$biome_name != 'Boreal Forests/Taiga',]
```

```{r}
cv.glm(birdlife_city_data_fixed_no_boreal, glm(formula = response ~ region_100km_ssm + region_50km_ssm + region_50km_elevation_delta + biome_name + population_growth, data = birdlife_city_data_fixed_no_boreal))$delta[1]
```

-- can we drop a variable?

```{r}
cv.glm(birdlife_city_data_fixed_no_boreal, glm(formula = response ~ region_50km_ssm + region_50km_elevation_delta + biome_name + population_growth, data = birdlife_city_data_fixed_no_boreal))$delta[1]
```

```{r}
cv.glm(birdlife_city_data_fixed_no_boreal, glm(formula = response ~ region_100km_ssm + region_50km_elevation_delta + biome_name + population_growth, data = birdlife_city_data_fixed_no_boreal))$delta[1]
```

```{r}
cv.glm(birdlife_city_data_fixed_no_boreal, glm(formula = response ~ region_100km_ssm + region_50km_ssm + biome_name + population_growth, data = birdlife_city_data_fixed_no_boreal))$delta[1]
```

```{r}
cv.glm(birdlife_city_data_fixed_no_boreal, glm(formula = response ~ region_100km_ssm + region_50km_ssm + region_50km_elevation_delta + population_growth, data = birdlife_city_data_fixed_no_boreal))$delta[1]
```

```{r}
cv.glm(birdlife_city_data_fixed_no_boreal, glm(formula = response ~ region_100km_ssm + region_50km_ssm + region_50km_elevation_delta + biome_name, data = birdlife_city_data_fixed_no_boreal))$delta[1]
```

-- drop biome_name to give CVE of 6.503421
-- can we drop another?

```{r}
cv.glm(birdlife_city_data_fixed_no_boreal, glm(formula = response ~ region_50km_ssm + region_50km_elevation_delta + population_growth, data = birdlife_city_data_fixed_no_boreal))$delta[1]
```

```{r}
cv.glm(birdlife_city_data_fixed_no_boreal, glm(formula = response ~ region_100km_ssm + region_50km_elevation_delta + population_growth, data = birdlife_city_data_fixed_no_boreal))$delta[1]
```


```{r}
cv.glm(birdlife_city_data_fixed_no_boreal, glm(formula = response ~ region_100km_ssm + region_50km_ssm + population_growth, data = birdlife_city_data_fixed_no_boreal))$delta[1]
```


```{r}
cv.glm(birdlife_city_data_fixed_no_boreal, glm(formula = response ~ region_100km_ssm + region_50km_ssm + region_50km_elevation_delta, data = birdlife_city_data_fixed_no_boreal))$delta[1]
```

-- drop region_100km_ssm to give CVE of 6.417311
-- can we drop another?

```{r}
cv.glm(birdlife_city_data_fixed_no_boreal, glm(formula = response ~ region_50km_elevation_delta + population_growth, data = birdlife_city_data_fixed_no_boreal))$delta[1]
```

```{r}
cv.glm(birdlife_city_data_fixed_no_boreal, glm(formula = response ~ region_50km_ssm + population_growth, data = birdlife_city_data_fixed_no_boreal))$delta[1]
```

```{r}
cv.glm(birdlife_city_data_fixed_no_boreal, glm(formula = response ~ region_50km_ssm + region_50km_elevation_delta, data = birdlife_city_data_fixed_no_boreal))$delta[1]
```

-- drop region_50km_elevation_delta to give CVE of 6.342025
-- can we drop another?

```{r}
cv.glm(birdlife_city_data_fixed_no_boreal, glm(formula = response ~ population_growth, data = birdlife_city_data_fixed_no_boreal))$delta[1]
```

```{r}
cv.glm(birdlife_city_data_fixed_no_boreal, glm(formula = response ~ region_50km_ssm, data = birdlife_city_data_fixed_no_boreal))$delta[1]
```

-- drop city_gdp_per_population to give CVE of 6.291299
-- is this better than no variable?

```{r}
cv.glm(birdlife_city_data_fixed_no_boreal, glm(formula = response ~ 1, data = birdlife_city_data_fixed_no_boreal))$delta[1]
```
-- yes, just!

----------------------------------------------------
-- so best model with birdlife is region_50km_ssm
----------------------------------------------------

```{r}
summary(glm(data = birdlife_city_data_fixed, formula = response ~ region_50km_ssm))
```

```{r}
reg_birdlife = glm(data = birdlife_city_data_fixed, formula = response ~ region_50km_ssm)
with(summary(reg_birdlife), 1 - deviance/null.deviance)
```


```{r}
ggplot(birdlife_city_data_named, aes(x = region_50km_ssm, y = response)) + geom_point() + geom_smooth(method = "glm")
```




------------------------
Check birdlife model fit
------------------------

```{r}
birdlife.fit <- glm(data = birdlife_city_data_fixed, formula = response ~ region_50km_ssm)
summary(birdlife.fit)
with(summary(birdlife.fit), 1 - deviance/null.deviance)
plot(birdlife.fit)
```

```{r}
birdlife_city_data_fixed_no_boreal[c(16, 53, 72), c("region_50km_ssm")]
```

```{r}
city_data[c(16, 53, 72), c("name", "region_50km_ssm")]
```

```{r}
dat <- predict(glm(formula = response ~ region_50km_ssm, data = birdlife_city_data_named), se.fit=T)

outside_se <- birdlife_city_data_named[birdlife_city_data_named$response < dat$fit - 15* dat$se.fit | birdlife_city_data_named$response > dat$fit + 15 * dat$se.fit,]

ggplot(birdlife_city_data_named, aes(x = region_50km_ssm, y = response)) + 
  geom_point(size=1) + 
  geom_smooth(method = "glm") +
  geom_text(aes(label = name), data = outside_se, size = 3, position = "dodge", vjust = "inward", hjust = "inward", color = "red", angle=-15) +
  geom_point(data = outside_se, color = "red") +
  theme_bw() +
  ylab("City Random Effect Intercept") + xlab("Regional (50km) SSM") + labs(title = "Birdlife")

ggsave("city_effect_richness__output__birdlife.jpg")
```

How much variation have we explained?
------------------------------------

```{r}
birdlife_city_data_named$residuals <- resid(birdlife.fit)
ggplot(birdlife_city_data_named, aes(y = response, x = residuals)) + 
  geom_point() +
  geom_smooth(method = "lm", se = F) +
  labs(title = "Birdlife", subtitle = paste("Correlation", cor(birdlife_city_data_named$residuals, birdlife_city_data_named$response))) +
  theme_bw()
```

------------------------
Check Merlin model fit
------------------------

```{r}
merlin.fit <- glm(data = merlin_city_data_named, formula = response ~ region_100km_ssm + region_50km_elevation_delta)
summary(merlin.fit)
with(summary(merlin.fit), 1 - deviance/null.deviance)
plot(merlin.fit)
```

```{r}
merlin_city_data_fixed_no_boreal[c(24, 42, 72), c("region_100km_ssm", "region_50km_elevation_delta")]
```

```{r}
city_data[c(24, 42, 72), c("name", "region_100km_ssm", "region_50km_elevation_delta")]
```

```{r}
ggplot(merlin_city_data_named, aes(x = region_100km_ssm, y = response)) + 
  geom_point(aes(size = region_50km_elevation_delta)) + 
  geom_smooth(method = "glm") +
  theme_bw() +
  theme(legend.position="bottom") +
  ylab("City Random Effect Intercept") + xlab("Regional (100km) SSM") + labs(title = "eBird") + guides(size=guide_legend(title="Regional (50km) Elevation Delta"))

ggsave("city_effect_richness__output__merlin.jpg")
```

How much variation have we explained?
------------------------------------
```{r}
merlin_city_data_named$residuals <- resid(merlin.fit)
ggplot(merlin_city_data_named, aes(y = response, x = residuals)) + 
  geom_point() +
  geom_smooth(method = "lm", se = F) +
  labs(title = "Merlin", subtitle = paste("Correlation", cor(merlin_city_data_named$residuals, merlin_city_data_named$response))) +
  theme_bw()
```


-------------------------
Check AIC
-------------------------

```{r}
AIC(
  glm(data = merlin_city_data_fixed, formula = response ~ region_100km_ssm + region_50km_ssm + region_50km_elevation_delta + biome_name + population_growth),
  glm(data = merlin_city_data_fixed, formula = response ~ region_100km_ssm + region_50km_elevation_delta)
)
```

```{r}
AIC(
  glm(data = birdlife_city_data_fixed, formula = response ~ region_100km_ssm + region_50km_ssm + region_50km_elevation_delta + biome_name + population_growth),
  glm(data = birdlife_city_data_fixed, formula = response ~ region_50km_ssm)
)
```



---------------------
LDG
----------------------
```{r}
birdlife_data_with_lat = fetch_city_data_for('birdlife', include_city_name = T)

dat2 <- predict(glm(formula = response ~ city_centre_latitude, data = birdlife_data_with_lat), se.fit=T)

outside_se <- birdlife_data_with_lat[birdlife_data_with_lat$response < dat2$fit - 15* dat2$se.fit | birdlife_data_with_lat$response > dat2$fit + 15 * dat2$se.fit,]

ggplot(birdlife_data_with_lat, aes(x = city_centre_latitude, y = response)) + 
  geom_point(size=1) + 
  geom_smooth(method = "glm", formula = y ~ I(x^2)) +
  geom_text(aes(label = name), data = outside_se, size = 3, position = "dodge", vjust = "inward", hjust = "inward", color = "red", angle=-15) +
  geom_point(data = outside_se, color = "red") +
  theme_bw() +
  ylab("City Random Effect Intercept") + xlab("Latitude (of city centre)") + labs(title = "Birdlife")

ggsave('city_effect_richness__output__ldg_birdlife.jpg')
```


```{r}
merlin_data_with_lat = fetch_city_data_for('merlin', include_city_name = T)

dat2 <- predict(glm(formula = response ~ city_centre_latitude, data = merlin_data_with_lat), se.fit=T)

outside_se <- merlin_data_with_lat[merlin_data_with_lat$response < dat2$fit - 15* dat2$se.fit | merlin_data_with_lat$response > dat2$fit + 15 * dat2$se.fit,]

ggplot(merlin_data_with_lat, aes(x = city_centre_latitude, y = response)) + 
  geom_point(size=1) + 
  geom_smooth(method = "glm", formula = y ~ I(x^2)) +
  geom_text(aes(label = name), data = outside_se, size = 3, position = "dodge", vjust = "inward", hjust = "inward", color = "red", angle=-15) +
  geom_point(data = outside_se, color = "red") +
  theme_bw() +
  ylab("City Random Effect Intercept") + xlab("Latitude (of city centre)") + labs(title = "eBird")

ggsave('city_effect_richness__output__ldg_merlin.jpg')
```